• Conditional Streamflow Probabilities

      Roefs, T. G.; Clainos, D. M.; Hydrology & Water Resources, University of Arizona (Arizona-Nevada Academy of Science, 1971-04-23)
      Streamflows of monthly or shorter time periods, are, in most parts of the world, conditionally dependent. In studies of planning, commitment and operation decisions concerning reservoirs, it is probably most computationally efficient to use simulation routines for decisions of low dimensions, as planning and commitment, and optimization routines for the highly dimensional operation rule decisions. This presents the major problem of combining the 2 routines, since streamflow dependencies in simulation routines are continuous while the direct stochastic optimization routines are discrete. A stochastic streamflow synthesis routine is described consisting of 2 parts: streamflow probability distribution and dependency analysis and a streamflow generation using the relationships developed. A discrete dependency matrix between streamflow amounts was then sought. Setting as the limits of interest the class 400-500 thousand acre ft in January and 500-600 thousand acre ft in February, and using the transforms specified, the appropriate normal deviates were determined. The next serious problem was calculating the conditional dependency based on the bivariate normal distribution. In order to calculate the joint probability exactly, double integrations would be required and these use too much computer time. For the problem addressed, therefore, the use of 1-dimensional conditional probabilities based on the flow interval midpoint is an adequate and effective procedure.
    • Optimal Utilization of Playa Lake Water in Irrigation

      Dvoracek, M. J.; Roefs, T. G.; Hydrology & Water Resources, University of Arizona (Arizona-Nevada Academy of Science, 1971-04-23)
      Playa lakes usually occur in arid or semiarid regions where lands are flat and there is an absence of well-developed surface drainage nets. They are usually filled by surface runoff from highly erratic precipitation patterns. There are about 20,000 of them in the high plains of Texas and their volume of storage is an estimated 2.5-3 maf. As such, they represent a major underutilized water source. The major drawbacks to their utilization are high evaporation losses, questionable depth-area relations and the stochastic nature of the rainfall source. This paper assumes that the water is available and presents a dynamic programming model useful in determining the optimal utilization of the water for irrigation. If irrigation is the major use, its timing of application is of paramount importance. A deterministic dynamic programming model, utilizing the state variables of antecedent soil moisture and amount of available water, is presented, and provides the time and amount of irrigation required to maximize crop response. A better stochastic model is also presented which considers rainfall probability and resulting lake filling. The models are only first attempts and do not incorporate all possible variables.
    • Recharging the Ogallala Formation Using Shallow Holes

      Dvoracek, M. J.; Peterson, S. H.; Hydrology & Water Resources, University of Arizona; Agricultural Engineering Department, Texas Tech University (Arizona-Nevada Academy of Science, 1971-04-23)
      The southern bed of the ogallala aquifer is hydrologically isolated from all outside areas of recharge, requiring local precipitation for all natural recharge. Current withdrawals are so much greater than natural recharge that it appears that artificial recharge affords the only means of establishing at least a pseudo-balance. A number of observation wells were drilled at Texas Tech University, and subsequently capped until recharge water became available. The initial recharge was 2.5 af over 12 days, at a rate of 120 gpm for about the first day, after which 60 gpm was relatively constant. Approximately 1 month later, 1.2 af were recharged over 3 days at rates ranging over 140-90 gpm. It became evident that a cavity was present at the bottom of the hole being recharged. On a later recharge occasion, the cavity seemed to have enlarged. During a period of 2 years more than 28 af of surface runoff water have been recharged through the shallow hole with increases in recharge rates for each subsequent recharge period. The nature of this phenomenon and the cavities are not understood. This may represent the long sought after answer to recharge of the aquifer, but much more extensive research needs to be done.
    • A Stochastic Analysis of Flows on Rillitto Creek

      Baran, N. E.; Kisiel, C. C.; Duckstein, L.; Hydrology & Water Resources, University of Arizona (Arizona-Nevada Academy of Science, 1971-04-23)
      In order to construct a simulation model for ephemeral streamflow and to examine in depth the problem of the worth of data for that model, measurements of the ephemeral streamflow of Rillitto creek, Tucson, were analyzed for the period 1933-1965. The simulation model was based on several hypotheses: (1) flow durations and their succeeding dry periods (time when no flow is present) are independent; (2) the distribution of the lengths of the dry periods and flows is stationary over a certain period of the year (summer); (3) stationary probability distributions for flow durations and for dry period lengths can be derived. A related problem was how to derive a simulation model for the total amount of flow (in acre-ft) within 1 flow period. Three variables were considered: flow duration (minutes), peak intensity of flow (cu ft/sec) and antecedent dry period-minutes (ADP). Because the assumption of variance constancy does not hold, a multiplicative regression model was used. Using an analysis of variance, which is described in detail, the worth of the 3 kinds of data were examined in relation to total flow. It was concluded that there are at least 5 times during the year when the flow intervals differ significantly, and the ADP is not important in determining flow volume because of the poison flow arrival rate in summer. Events occur at random and are not clustered as in summer, indicating that channel moisture does not differ much between flow events.